Single Inductance Loop Detectors (ILDs) which provide online measurements of traffic
volume and occupancy are widely used devices in road systems. Due to the nature of traffic
flow, fast estimation and forecasting of vehicular speed using the data collected by an ILD are
crucial to online road traffic management. In this paper statistical inference for vehicular
speed is formulated as a dynamic generalized linear model with a reciprocal inverse Gaussian
observational distribution. The formulation motivates us to extend the Gaussian Kalman filter
to this non-Gaussian scenario. This results in a set of simple recursive formulae where the
current estimate of the parameter of interest is updated as a weighted harmonic average of the
previous estimate and the current observation. By applying the developed non-Gaussian
Kalman filter to analyze traffic data collected by an ILD, we provide a competitive alternative
to estimate vehicular speed at a minimum computational cost.